The Mazur intersection property and Asplund spaces
| dc.contributor.author | Jiménez Sevilla, María Del Mar | |
| dc.contributor.author | Moreno, José Pedro | |
| dc.date.accessioned | 2023-06-20T18:49:50Z | |
| dc.date.available | 2023-06-20T18:49:50Z | |
| dc.date.issued | 1995 | |
| dc.description.abstract | We answer a question posed by J. R. Giles, D. A. Gregory and B. Sims, on the Mazur intersection property, by exhibiting a class of non Asplund spaces admitting an equivalent norm with the above property. On the other hand, if the continuum hypothesis is assumed, we nd an Asplund space admitting no equivalent norm with the Mazur intersection property and whose dual space admits no equivalent norm with the weak* Mazur intersection property. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/22710 | |
| dc.identifier.issn | 0764-4442 | |
| dc.identifier.officialurl | http://www.refdoc.fr/Detailnotice?idarticle=16138734 | |
| dc.identifier.relatedurl | http://www.elsevier.com/journals/comptes-rendus-mathematique/1631-073X | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/58721 | |
| dc.issue.number | 9 | |
| dc.journal.title | Comptes Rendus de l'Académie des Sciences. Série I. Mathématique | |
| dc.language.iso | eng | |
| dc.page.final | 1223 | |
| dc.page.initial | 1219 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PB 93-0452 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517 | |
| dc.subject.keyword | Mazur intersection property | |
| dc.subject.keyword | Non-Asplund spaces | |
| dc.subject.keyword | Equivalent norm | |
| dc.subject.keyword | Weak* Mazur intersection property | |
| dc.subject.ucm | Análisis matemático | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | The Mazur intersection property and Asplund spaces | |
| dc.type | journal article | |
| dc.volume.number | 321 | |
| dcterms.references | Dongjian Chen, Zhibao Hu, and Bor-Luh Lin, Balls intersection properties of Banach spaces, Bull. Austral. Math. Soc. 45 (1992), 333-342. R. Deville, Un th�eoreme de transfert pour la propri�et�e des boules, Canad. Math. Bull. 30 (1987), 295-300. R. Deville, G. Godefroy, and V. Zizler, Smoothness and renormings in Banach spaces, vol. 64, Pitman Monograph and Surveys in Pure and Applied Mathematics, 1993. G. A. Edgar, A long James space, Lecture notes in Math., vol. 794, 1979. P. G. Georgiev, Mazur's intersection property and a Krein-Milman type theorem for almost all closed, convex and bounded subsets of a Banach space, Proc. Am. Math. Soc. 104 (1988), 157-164. On the residuality of the set of norms having Mazur's intersection property,Mathematica Balkanica 5 (1991), 20-26. J. R. Giles, D. A. Gregory, and B. Sims, Characterization of normed linear spaces with Mazur's intersection property, Bull. Austral. Math. Soc. 18 (1978), 471-476. R. G. Haydon, A counterexample to several questions about scattered compact spaces, Bull. London Math. Soc. 22 (1990), 261-268. P. S. Kenderov and J. R. Giles, On the structure of Banach spaces with Mazur's intersection property, Math. Ann. 291 (1991), 463-473. S. Mazur, � Uber schwache Konvergentz in den Raumen lp, Studia Math. 4 (1933), 128{133. J. P. Moreno, Geometry of Banach spaces with (�; ")-property or (�; ")- property, Rocky Mountain J. Math., to appear. On the weak* Mazur intersection property and Fr�echet di�erentiable norms on dense open sets, Preprint. S. Negrepontis, Banach spaces and topology, Handbook of set theoretic Topology(K. Kunen and J. E. Vaughan , eds.), 1984. R. R. Phelps, A representation theorem for bounded convex sets, Proc. Am. Math. Soc. 11 (1960), 976-983. S. Troyanski, On locally uniformly convex and di�erentiable norms in certain non separable Banach spaces, Studia Math. 37 (1971), 173-180. V. Zizler, Renormings concerning the Mazur intersection property of balls for weakly compact convex sets, Math. Ann. 276 (1986), 61-66. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 | |
| relation.isAuthorOfPublication.latestForDiscovery | 36c2a4e7-ac6d-450d-b64c-692a94ff6361 |
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